Bernd Thaller

Visualization of complex-valued functions

Index:

Click on any of the icons below to see a full-sized image (JPEG, each about 30k).

f(z) = z
(=color map)

f(z)=1/z

f(z)=1/z2

f(z)=1/(z5-1)

f(z) = z/conj(z)

f(z) = sqrt(z)

f(z) = z3/2

f(z) = ln(z)

f(z) = exp(z)

f(z) = exp(1/z)

f(z) = sin(z)

f(z) = tan(z)

f(z) = arctan(z)

f(z) = artanh(z)

f(z) = gamma(z)

f(z) = erf(1/z)

f(z) = zeta(z)

f(z) = J0(z)+iY0(z)

These plots have been generated with Mathematica using the package ComplexPlot.m. This package uses a mapping of the compactified complex plane onto the surface of the color manifold in the HLS color model. This mapping can be described as a stereographic projection. A similar (but not the same) color map is described on John L. Richardson's page about visualization.